Definition of FUNCTIONS. Meaning of FUNCTIONS. Synonyms of FUNCTIONS
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Definition of FUNCTIONS
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Calculus of functions Calculus Cal"cu*lus, n.; pl. Calculi. [L, calculus. See
Calculate, and Calcule.]
1. (Med.) Any solid concretion, formed in any part of the
body, but most frequent in the organs that act as
reservoirs, and in the passages connected with them; as,
biliary calculi; urinary calculi, etc.
2. (Math.) A method of computation; any process of reasoning
by the use of symbols; any branch of mathematics that may
involve calculation.
Barycentric calculus, a method of treating geometry by
defining a point as the center of gravity of certain other
points to which co["e]fficients or weights are ascribed.
Calculus of functions, that branch of mathematics which
treats of the forms of functions that shall satisfy given
conditions.
Calculus of operations, that branch of mathematical logic
that treats of all operations that satisfy given
conditions.
Calculus of probabilities, the science that treats of the
computation of the probabilities of events, or the
application of numbers to chance.
Calculus of variations, a branch of mathematics in which
the laws of dependence which bind the variable quantities
together are themselves subject to change.
Differential calculus, a method of investigating
mathematical questions by using the ratio of certain
indefinitely small quantities called differentials. The
problems are primarily of this form: to find how the
change in some variable quantity alters at each instant
the value of a quantity dependent upon it.
Exponential calculus, that part of algebra which treats of
exponents.
Imaginary calculus, a method of investigating the relations
of real or imaginary quantities by the use of the
imaginary symbols and quantities of algebra.
Integral calculus, a method which in the reverse of the
differential, the primary object of which is to learn from
the known ratio of the indefinitely small changes of two
or more magnitudes, the relation of the magnitudes
themselves, or, in other words, from having the
differential of an algebraic expression to find the
expression itself.
Circular functions Circular Cir"cu*lar, a. [L. circularis, fr. circulus circle:
cf. F. circulaire. See Circle.]
1. In the form of, or bounded by, a circle; round.
2. repeating itself; ending in itself; reverting to the point
of beginning; hence, illogical; inconclusive; as, circular
reasoning.
3. Adhering to a fixed circle of legends; cyclic; hence,
mean; inferior. See Cyclic poets, under Cyclic.
Had Virgil been a circular poet, and closely adhered
to history, how could the Romans have had Dido?
--Dennis.
4. Addressed to a circle, or to a number of persons having a
common interest; circulated, or intended for circulation;
as, a circular letter.
A proclamation of Henry III., . . . doubtless
circular throughout England. --Hallam.
5. Perfect; complete. [Obs.]
A man so absolute and circular In all those
wished-for rarities that may take A virgin captive.
--Massinger.
Circular are, any portion of the circumference of a circle.
Circular cubics (Math.), curves of the third order which
are imagined to pass through the two circular points at
infinity.
Circular functions. (Math.) See under Function.
Circular instruments, mathematical instruments employed for
measuring angles, in which the graduation extends round
the whole circumference of a circle, or 360[deg].
Circular lines, straight lines pertaining to the circle, as
sines, tangents, secants, etc.
Circularnote or letter.
(a) (Com.) See under Credit.
(b) (Diplomacy) A letter addressed in identical terms to a
number of persons.
Circular numbers (Arith.), those whose powers terminate in
the same digits as the roots themselves; as 5 and 6, whose
squares are 25 and 36. --Bailey. --Barlow.
Circular points at infinity (Geom.), two imaginary points
at infinite distance through which every circle in the
plane is, in the theory of curves, imagined to pass.
Circular polarization. (Min.) See under Polarization.
Circular or Globularsailing (Naut.), the method of
sailing by the arc of a great circle.
Circular saw. See under Saw.
Hyperbolic functions Hyperbolic Hy`per*bol"ic, Hyperbolical Hy`per*bol"ic*al, a.
[L. hyperbolicus, Gr. ?: cf. F. hyperbolique.]
1. (Math.) Belonging to the hyperbola; having the nature of
the hyperbola.
2. (Rhet.) Relating to, containing, or of the nature of,
hyperbole; exaggerating or diminishing beyond the fact;
exceeding the truth; as, an hyperbolical expression.
``This hyperbolical epitaph.' --Fuller.
Hyperbolic functions (Math.), certain functions which have
relations to the hyperbola corresponding to those which
sines, cosines, tangents, etc., have to the circle; and
hence, called hyperbolic sines, hyperbolic cosines,
etc.
Hyperbolic logarithm. See Logarithm.
Hyperbolic spiral (Math.), a spiral curve, the law of which
is, that the distance from the pole to the generating
point varies inversely as the angle swept over by the
radius vector.
Sustentative functions Sustentative Sus"ten*ta*tive, a.
Adapted to sustain, strengthen, or corroborate; as,
sustentative citations or quotations.
Sustentative functions (Physiol.), those functions of the
body which affect its material composition and thus
determine its mass.
Vital functions Vital Vi"tal, a. [F., fr. L. vitalis, fr. vita life; akin to
vivere to live. See Vivid.]
1. Belonging or relating to life, either animal or vegetable;
as, vital energies; vital functions; vital actions.
2. Contributing to life; necessary to, or supporting, life;
as, vital blood.
Do the heavens afford him vital food? --Spenser.
And vital virtue infused, and vital warmth.
--Milton.
3. Containing life; living. ``Spirits that live throughout,
vital in every part.' --Milton.
4. Being the seat of life; being that on which life depends;
mortal.
The dart flew on, and pierced a vital part. --Pope.
5. Very necessary; highly important; essential.
A competence is vital to content. --Young.
6. Capable of living; in a state to live; viable. [R.]
Pythagoras and Hippocrates . . . affirm the birth of
the seventh month to be vital. --Sir T.
Browne.
Vital air, oxygen gas; -- so called because essential to
animal life. [Obs.]
Vital capacity (Physiol.), the breathing capacity of the
lungs; -- expressed by the number of cubic inches of air
which can be forcibly exhaled after a full inspiration.
Vital force. (Biol.) See under Force. The vital forces,
according to Cope, are nerve force (neurism), growth force
(bathmism), and thought force (phrenism), all under the
direction and control of the vital principle. Apart from
the phenomena of consciousness, vital actions no longer
need to be considered as of a mysterious and unfathomable
character, nor vital force as anything other than a form
of physical energy derived from, and convertible into,
other well-known forces of nature.
Vital functions (Physiol.), those functions or actions of
the body on which life is directly dependent, as the
circulation of the blood, digestion, etc.
Vital principle, an immaterial force, to which the
functions peculiar to living beings are ascribed.
Vital statistics, statistics respecting the duration of
life, and the circumstances affecting its duration.
Vital tripod. (Physiol.) See under Tripod.
Vital vessels (Bot.), a name for latex tubes, now disused.
See Latex.
